Question

A triangle with an angle measure of 40° was cut into 6 triangles by its angle bisectors. Some of these new triangles are right triangles. What could be the measure of the largest angle of this triangle?

Answer 1

100-140

Explanation:

Here's the explanation: 1. The angle bisectors of a triangle divide each angle of the triangle into two congruent angles. 2. Since the triangle has an angle measure of 40°, each angle bisector would create two angles measuring 20° each. 3. When a triangle is divided by its angle bisectors, the resulting triangles have one of the original angles as their vertex angle. 4. In this case, the vertex angle of the resulting triangles would be 40°. 5. A right triangle is formed when one of its angles measures 90°. To form a right triangle, one of the resulting triangles must have a vertex angle of 90°. 6. For this to occur, one of the original angles must be greater than 100° but less than 140°. 7. Therefore, the measure of the largest angle of the original triangle can be any value between 100° and 140°.